July 2, 1908] 



NA TURE 



211 



ditions in the system. The method of treatment will not 

 be essentially different from that which will be applied 

 later to the more general problem, but we have pro- 

 visionally to be content with introducing the two following 

 simplifications : — 



(i) We will assume that the mixture is the same through- 

 out the whole of the system. 



(2) We will not treat the different galactic latitudes 

 separately. 



The consequence will be that the resulting variations of 

 density to which our discussion leads will not represent 

 the actual variations which we Avould find if we travelled 

 in space in any determined fixed direction, but a variation 

 which will represent some average of what we would find 

 on all our travels if we successively directed them to 

 different regions of the sky. 



Our present problem will thus be confined to finding 

 out : — 



(a) The mixture law. 



(b) The mean star-density at different distances from the 

 solar system. 



If time allows, I will, at the end of this lecture, say a 

 few words on- the restrictions introduced, and the way to 

 get rid of them. 



As it is not given to us to make such travels through 

 space as here imagined, we have to rely on more human 

 methods for the solution of our problem. 



Determination of Distance. 



It is at once evident that there would be no difficulty 

 at all if it were as easy to determine the distance of the 

 stars as it is to determine the direction in which they 

 stand. For in that case the stars would be localised in 

 space, and it would be possible to construct a true model 

 from which the peculiarities of the system might be 

 studied. 



It is a fact, however, that, with the exception of a 

 hundred stars at most, we know nothing of the distances 

 of the individual stars. 



What is the cause of this state of things? It is owing 

 to the fact that we have two eyes that we are enabled 

 not only to perceive the direction in which external objects 

 are situated, but to get an idea of their distance, to localise 

 them in space. But this power is rather limited. For 

 distances exceeding some hundreds of yards it- utterly fails. 

 The reason is that the distance between the eyes as com- 

 pared with the distance to be evaluated becomes too small. 

 Instruments have been devised by which the distance 

 between the eyes is, as it were, artificially increased. 

 With a good instrument of this sort distances of several 

 miles may be evaluated. For still greater distances we 

 may imagine each eye replaced by a photographic plate. 

 This would even already be quite sufficient for one of the 

 heavenly bodies, viz. for the moon. 



At one and the same moment let a photograph of the 

 moon and the surrounding stars be taken both at the Cape 

 Observatory and at the Royal Observatory at Greenwich. 

 Placing the two photographs side by side in the stereo- 

 scope, we shall clearly see the moon " hanging in space," 

 and may evaluate its distance. 



But already for the sun and the nearest planets, our 

 next neighbours in the universe after the moon, the 

 difficulty re-commences. 



The reason is that any available distance on the earth, 

 taken as eye-distance, is rather small for the purpose. 

 However, owing to incredible perseverance and skill of 

 several observers, and by substituting the most refined 

 measurement for stereoscopic examination, astronomers 

 have succeeded in overcoming the difficulty for the sun. 

 I think we may sav that at present we know its distance 

 to within a thousandth part of its amount. Knowing the 

 sun's distance, we get that of all the planets by a well- 

 known relation existing between the planetary distances. 



But now for the fixed stars, which must be hundreds 

 of thousands of times further removed than the sun. 

 There evidently can be no question of any sufficient eye- 

 distance on our earth. Meanwhile, our success with the 

 sun has provided us with a new eye-distance, 24,000 times 

 greater than any possible eye-distance on the earth. For 

 now that we know the distance at which the earth travels 

 In its orbit round the sun, we can take the diameter of its 

 orbit as our eye-distance. Photographs taken at epochs 



NO. 2018, VOL. 78I 



six months apart will represent the stellar world as seen 

 from points the distance between which is already best 

 expressed in the time it would take light to traverse it. 

 The time would be about sixteen minutes. 



However, even this distance, immense as it is, is on 

 the whole inadequate for obtaining a stereoscopic view of 

 the stars. It is only in quite exceptional cases that photo- 

 graphs on a large scale — that is, obtained by the aid of 

 big telescopes — show any stereoscopic effect for fixed stars. 

 By accurate measurement of the photos we may perhaps 

 get somewhat beyond what we can attain by simple stereo- 

 scopic inspection, but, as we said a moment ago, astro- 

 nomers have not succeeded in this way in determining 

 the distance of more than a hundred stars in all. 



How far we are still from getting good stereoscopic 

 views appears clearly from the stereoscopic maps which 

 vour countryman, Mr. Heath, constructed, making use of 

 the data obtained in the way presently to be considered. 

 In order to get really good pictures, he found it necessary 

 to increase the eye-distance furnished by the earth's orbit 

 19,000 times. Are there, then, no means of still increasing 

 this eye-distance? 



Motion of Solar System through Space. 



There is one way, but it is a rather imperfect one. Sir 

 William Herschel was the first to show, though certainly 

 his data were still hardly sufficient for the purpose, that 

 the whole of the solar system is moving through space 

 in the direction towards the constellation of Hercules. 

 Later observations and computations have confirmed 

 Herschel 's conclusions, and we have even been able of late 

 to fix with some precision the velocity of this motion, 

 which amounts to 20 kilometres per second. This velocity 

 is a 15,000th part of the velocity of light. In the 150 

 years elapsed since Bradley determined for the first time 

 the position of numerous stars with modern precision, the 

 solar system must thus have covered a distance of exactly 

 a hundredth part of a light-year, i.e. we are thus enabled 

 to make pictures of the sky as seen from points of view 

 at a mutual distance of a hundredth of a light-year. Our 

 eye-distance of sixteen light minutes is thus increased 

 more than 300-fold. True, this distance falls still con- 

 siderably short of that adopted by Heath, but it appears 

 that, for a considerable part of the stars, it is, though not 

 nearly so great as might be desired, still in a certain way 

 sufficient. 



There is, however, a difficulty in the way, which prevents 

 our pictures from giving a stereoscopic view of the stars 

 at all, and thus prevents the determination of the distance 

 of any star in this manner. The difficulty is that the 

 changed directions in which, after the lapse of 150 years, 

 we see the stars is not exclusively the consequence of the 

 sun's motion through space, but is due also to a real 

 motion of the stars themselves. The two causes of dis- 

 placement which, in the case that we take the diameter 

 of the earth's orbit as eye-distance, are separable by means 

 of a simple device, become inseparable in the present case. 

 In order to see whether this difficulty be or be not abso- 

 lutely insuperable, I will take a parallel case on the earth. 



At a certain distance we observe a cloud of insects 

 hovering over a small pond. In order to evaluate the 

 distance separating the insects from our eye, suppose that 

 we make a photograph ; then, after a few seconds, a 

 second one from a slightly different standpoint. It must 

 be evident that even if we have used an instrument which 

 clearly shows the individual insects, the two pictures put 

 in the stereoscope will not furnish a stereoscopic view of 

 them individually : on the contrary, the picture as seen in 

 the stereoscope will be perfectly chaotic. The reason, of 

 course, is that in the interval between the taking of the 

 two photographs the insects have moved. Does it follow 

 that no evaluation of the distance can be obtained? 



The answer must be, of any individual insect, no ; but 

 of the cloud, as a whole, we can evaluate its distance pro- 

 vided that the cloud, as a whole, has not moved ; or, 

 expressed more mathematically, provided that the centre of 

 gravity of the cloud has not moved, we can derive the 

 average distance ' of all the insects. We shall be sure of 



1 The expression awra^ct/M/aufc ougtit, strictly speaking, to be replarfrf 

 by the distance corresponding to the average faralla.x. For clearness sake 

 I have ventured here and in what follows to substitute one expression for th 

 other. 



